And how would it pertain to performance and memory issues? Is it more a problem on AIX than Solaris or Windows?
A mutex is just a lock. Like the lock on a portapotty - makes sure only one person uses it at a time. There are many types of mutual exclusion, for a good overview you should check out Operating Systems: Design and Implementation by Andrew S. Tanenbaum or osdev.org. I have never heard of a "split mutex" before, and Google returns nothing. However, the term "split" suggests that it is shared hence not mutually excluded (multiple people in the portapotty), which doesn't quite make sense.
Usually you don't have to worry about mutexes unless you are designing an operating system or a device driver. And the only way they would affect performance is if the resource being locked is in high demand by other processes (i.e. there's a big line-up for the portapotty).
Unless you have some extenuating situations like SMP, etc. it is best to leave it up to the operating system to decide how to handle mutexes and resources, as that's what its there fore.
I'm sorry I couldn't be of more assistance. I don't know anything about "split" mutexes. If its specific to AIX you might want to check IBM manuals, otherwise there might be able to find something in some IEEE research papers.
UPDATE: Upon further investigation, this seems to be a case of common case optimization. The mutex is "split" into two cases: 1) the common case where nothing special is needed, some safety checks can be assumed or kernel functions bypassed called the fastpath or 2) we can't assume that the checks pass or cannot do certain optimizations, called the slowpath. Amdahl's law is often used to quantify such case optimization.